Power equation: P = I²R
Power = (current)² × resistance. In symbols, P = I² R. P is the power in watts (W), I is the current in amperes (A) and R is the resistance in ohms (Ω). All three boards print it in this form for Physics and Combined Science, and it is on the equation sheet in every GCSE physics paper.
Equation
P = I² R
| Symbol | Quantity | Unit |
|---|---|---|
P | power | W |
I | current | A |
R | resistance | Ω |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | P = I² R |
| AQA Combined Science (8464) | Recall | P = I² R |
| Edexcel Physics (1PH0) | Recall | P = I² R |
| Edexcel Combined Science (1SC0) | Recall | P = I² R |
| OCR Gateway Physics A (J249) | Recall | P = I² R |
| OCR Twenty First Century Physics B (J259) | Recall | P = I² R |
Calculator: P = I² R
Why the current is squared
When current flows through a resistor, the charges bump into the atoms of the metal. That makes the resistor warm up. P = I² R tells you how many joules of heating happen each second.
The current appears twice. A bigger current means more charge passing each second, and each coulomb also loses more energy, because the p.d. across the resistor is bigger too. Double the current and the heating goes up four times.
This heating is how a fuse works. A thin wire inside it gets hotter as the current rises, and above its rating the wire melts and breaks the circuit.
Board forms
AQA, Edexcel and OCR use the same symbols: P = I² R. AQA and OCR word it as power = (current)² × resistance, and Edexcel calls it electrical power. Every specification lists it for recall. The exam sheet shows it for each series from 2025, and the AQA equation list is one place to see it with its neighbours.
You can get it from two other equations on the same list. Start with P = VI and swap V for I R from V = IR.
Rearranging P = I²R
- R = P ÷ I²
- I = √(P ÷ R)
This equation explains why the National Grid sends electricity at a very high p.d. For the same power, a higher p.d. means a smaller current, and a smaller current wastes far less energy heating the cables. Transformers do the change, as the transformer power equation shows.
Worked examples
P
- P = I² R
- P = 3² × 8
- P = 9 × 8
- P = 72 W
72 W
R
- Change the current to amps: 500 mA = 0.5 A
- R = P ÷ I²
- R = 1.5 ÷ 0.5²
- R = 1.5 ÷ 0.25
- R = 6 Ω
6 Ω
I
- I = √(P ÷ R)
- I = √(100 ÷ 25)
- I = √4
- I = 2 A
2 A
Common mistakes
- Multiplying I by R and then squaring the lot. Only the current is squared, so find I² before you multiply by R.
- Squaring 500 instead of 0.5. Convert milliamps to amps first, because 500² gives a power a million times too big.
- Stopping at I² when you solve for current. If you get 4 for a question about current, take the square root to get 2 A.
- Using P = I² R when the question gives p.d. and current but no resistance. Pick P = V I in that case.
Try getting I on its own from P = I²R, square root and all, in the Equation Rearranger.
Questions people ask
When should I use P = I²R instead of P = VI?
Use P = I² R when you know the current and the resistance. Use P = V I when you know the p.d. and the current.
Is the heating from P = I²R always wasted?
No. In a kettle, toaster or electric heater, that heating is the useful output. In cables and phone chargers it is wasted energy.